Here is a sample of pulse rates for females.
100, 97, 90, 88, 83, 82, 80, 80, 78, 77, 73, 72, 70, 69, 68, 67, 67, 60, 60, 60
1) Find n, x-bar, sx and the median.
2) Is -0.5 < z(median) < 0.5?
3) is proportion(z(high)) - proportion(z(low)) > 88%?
4) If yes to both question 2) and question 3), Find the 95% confidence interval for mux, where the endpoints are rounded to one place after the decimal point.
5) Find the 95% confidence interval for sigmax.
Answers in the comments.
100, 97, 90, 88, 83, 82, 80, 80, 78, 77, 73, 72, 70, 69, 68, 67, 67, 60, 60, 60
ReplyDelete1) Find n, x-bar, sx and the median.
n = 20.
x-bar = 76.1
s_x = 11.7
median = 75
2) Is -0.5 < z(median) < 0.5?
(75-76.1)/11.7 = -.09, so okay.
3) is proportion(z(high)) - proportion(z(low)) > 88%?
z(100) = (100-76.1)/11.7 = 2.04
z(60) = (60-76.1)/11.7 = -1.38
2.04 corresponds to .9793
-1.38 corresponds to .0838
.9793 - .0838 = .8955, so okay.
4) If yes to both question 2) and question 3), Find the 95% confidence interval for mux, where the endpoints are rounded to one place after the decimal point.
n = 20, so df = 19 and CLM_95% = 2.093
76.1 - 2.093*11.7/sqrt(20) = 70.6
76.1 + 2.093*11.7/sqrt(20) = 81.6
70.6 < mu_x < 81.6 is the 95% confidence interval.
5) Find the 95% confidence interval for sigma_x.
chi square left = 8.907
chi square right = 32.852
11.7*sqrt(19/8.907) = 17.1
11.7*sqrt(19/32.852) = 8.9
8.9 < sigma_x < 17.1 is the 95% confidence interval.